No such correspondence is visible. My no has been supported.
This is the problem I have with your "no"s. It remains unclear what your point is, where and why you disagree with my claims. Why not simply explaining, whenever you write "no", what is the particular statement you disagree with, and what is the IYO correct/corrected variant you agree with? I would guess in 65% I would simply react with "ok, no problem", and a minor correction.
I'll try again, as above: A commons is a resource that was not produced and has no owner. It is not a good or service made available to everyone by its owner, like a public library, or produced by an economy and distributed around so anyone can own some, like a grade school education. It is not a common good, something produced or owned. The example Hardin used was open, ungoverned, unowned grassland used for grazing cattle by anyone who wanted to. One can contrast that with the public grazing lands owned by the US government, the communal grazing lands owned by ejidos or similar in some places, and the privately owned pastures of ranchers in market economies. Other people have used air, airspace, fresh water from rainfall, populations of wild animals and plants, minerals, and the like.
Ok, so I can explain that, because I care about the economic problem, I can see no difference between unowned grassland and grassland "open to public grazing" (which I interpret here, without knowing how US handles this, as free access to everybody who wants to use it for grazing) owned by the US government. The formal ownership is not what matters if there is an economic problem. What would make a difference is if the US government would behave like a private owner - thus, would protect it against use without permission and require payments for permission. If the use, instead, remains open for all and for free, the US ownership changes nothing.
The difference between things which have to be produced and things which exist, but not in a sufficiently large amount so that overuse becomes a problem, is also in most of the cases irrelevant for the economic problem.
Ownership is a legal status. You have to have laws, contract enforcement, etc. - government.
This is one meaning of the word "ownership", and in many economic problems an irrelevant one. Of course, a stateless society based on a free market has ownership too. And, of course, all the illegal things which exists against the will of the state, who tells that nobody should own them, are usually also owned by well-defined persons - and the judges in such criminal cases try hard to establish who was the owner. Children own their pocket money and what they buy for them - even if legally they don't.
(And, of course, there is the other side - the "people" have been declared to "own" almost everything in socialist states, but in fact all this was "owned" in a non-legal meaning by particular party leaders. All of this "ownership" being informal. But this informality is not the main economic problem of such states - more serious is insecurity: Tomorrow, another guy may becomes the owner of everything you own, because he is a better friend of the Great Leader. This makes the time preference for using this "property" rather short: Take all you can, transfer it to a safe bank account in the West - the actual form of this ownership in the Nazi-Ukraine)
So, there is a lot of ownership in the world without a state, even against the state. Thus, if real (not formal) ownership allows to solve a common good or commons problem, it can be solved also without the state.
The produced/not produced difference makes also no difference - with group ownership of the produced thinks, restriction of their use to the members, and entry fees or membership fees to get the resources for this one can solve various common good problems with things which have to be produced. The same technique - group ownership with fees, now intended to prevent overuse of unproduced things, can solve the same problem for unproduced things too.
Things produced by somebody and made available for free use by the public are, in itself, not a problem at all. It is his decision to do this, fine. The problem appears if it would be impossible to make it available for a fee. Typical solutions of such problem are moral enumerations to those who provide it, restrictions of the payments to regular users. Say, building local streets could be paid by the people living in the neighbourhood: There would be, yet, a common good problem, but a solvable one once the environment is not that big. All the guests and travellers and so on can use all this for free.
Very little in the way of most commons is ever going to be the result of somebody's labor - how would the resource have existed before? And you have omitted the actual process by which the clarity and visibility of one's ownership is established - so that one can, say, borrow money with the property as collateral. That process requires a government - might even be said to define a government.
All one needs for using this method to establish ownership is that there has to be some investment which improves the part of the commons which is claimed. The classical example is cleaning it to make its use for agriculture possible. Or irrigation. This defines a quite natural process of property creation - one improves as much as one needs and then owns it. The costs for improvement limit the amount of what one can own in such a way.
For ownership to become ownership it is sufficient that the relevant community accepts it as ownership. Then, it can be also rented or exchanged, with the corresponding contracts being enforced by the local reputational system. So, no, it does not require a government, it requires only a way to enforce contracts.
Hernando de Soto, among others, has written extensively on the consequences of various ways in which governments have established ownership of real estate, the extraordinary and underappreciated influence of the technical details involved in owning a piece of land with a house on it, and the burden of governmental failure or dysfunction.
A major government dysfunction is actually simply not to accept the traditional ownership rights of local communities. So, if a rich enough Western firm wants to buy the land, they can by it and the owners have to be happy if they have enough time to run away. And, of course, in such societies the Big Banks supported by the government cannot give credits with such unaccepted ownership as security, because they would receive only unaccepted land.
All agricultural and herding societies that have lasted long enough to be recorded have devoted considerable political effort to governing that commons, because the consequences of not governing it are indeed a Tragedy. Some theorist believe that was the reason governments were invented.
Maybe this is part of the explanation. But if governments would restrict themself to governing commons where no better ownership-based solutions are possible, I think no libertarian would object against them, I think. The most plausible explanation for state creation remains conquest: A strong military can conquer neighours and enslave them.